Here, \(n_{\rm det}\)  distinguishes between experiments that aim at detecting the stochastic GW background by means of an auto-correlation (\(n_{\rm det} = 1\) ) or a cross-correlation (\(n_{\rm det} = 2\) ) measurement.
The \(n_{\rm det} = 1\)  case refers to situations where an experiment consists of just one detector, while the \(n_{\rm det} = 2\)  case refers to situations where it is possible to cross-correlate the two signals of a detector pair within a detector network.
Further below, we will specifically consider three satellite-borne GW interferometers: the Laser Interferometer Space Antenna (LISA) [1]}, [2]}, the Deci-Hertz Interferometer Gravitational-Wave Observatory (DECIGO) [3]}, [4]}, [5]}, [6]}, and the Big-Bang Observer (BBO) [7]}, [8]}, [9]}.
Given the envisaged configuration of these experiments, we will set \(n_{\rm det} = 1\)  for LISA and \(n_{\rm det} = 2\)  for DECIGO and BBO.
For a discussion of the noise spectra of these experiments, we refer the reader to the Appendix of Ref. [10]}.
